RRT-Connect: An Efficient Approach to Single-Query Path Planning - PowerPoint PPT Presentation

RRT-Connect: An Efficient Approach to Single-Query Path Planning James J. Kuffner, Jr. Steven M. LaValle ICRA 2000 Presented by Manel Baradad 6.882 Embodied Intelligence Spring 2020

Problem Single-query path planning, from start to goal. In “high-dimensional” configuration spaces Find path from A to B Move an object: from State A to State B 2

Two Ingredients ● Rapidly-exploring random trees (RRT): ● 2 x RRT: One from start and one from goal Greedy Heuristic to connect them RRT Exploration 3

Rapidly-exploring random trees (RRT’s) K = 0 4

Rapidly-exploring random trees (RRT’s) K = T 5

Rapidly-exploring random trees (RRT’s) K = T q sampled uniformly at random over all space 6

Rapidly-exploring random trees (RRT’s) K = T Closest to q in the actual graph 7

Rapidly-exploring random trees (RRT’s) K = T q new :closest to q within Ɛ from q near 8 If no q new, repeat random q

Rapidly-exploring random trees (RRT’s) Repeat for K = T + 1 9

Rapidly-exploring random trees (RRT’s) Simple uniform sampling of q favors exploration P(node being q near ) ~ size of the Voronoi region ~ unexplored region 10

Rapidly-exploring random trees (RRT’s) Simple uniform sampling of q favors exploration P(node being q near ) ~ size of the Voronoi region ~ unexplored region High P of being q near Low P of being q near 11

2 x RRT How to dig a tunnel from A to B? Just start caving from each side Worse case you have two tunnels! Just build two RRT’s from start and goal. Have some attracting heuristic so that they meet. 12

RRT-Connect K = 0 13

RRT-Connect K = T 14

RRT-Connect K = T q at random uniformly 15

RRT-Connect K = T 16

RRT-Connect K = T 17

RRT-Connect K = T Connect B : Previous q new acts as q for B 18

RRT-Connect K = T Connect B : Previous q new acts as q for B 19

RRT-Connect K = T 20

RRT-Connect K = T + 1 Repeat, swapping behavior between A and B 21

Examples 22

Improvement: RRT* Idea: store and use a cost per node (distance to A/B). 1) Expand minimum costs: ~When adding nodes, add the ones of minimum cost. 23

Improvement: RRT* Idea: store and use a cost per node (distance to A/B). 2) Update costs: ~When a new node is added, look in its neighborhood to see if the tree can be rewired to reduce costs q new q new q A q A 24

RRT-connect A* (Shakey paper) Randomized Non-randomized Greedy heuristic Admissible heuristic Suboptimal Optimal Faster for “typical“ problems Slower but optimal 25

Open question Would it be useful to have N RTTs expanded from N states instead of just 2 (start and goal)? What these states would correspond to? How much could it be parallelized? 26